2. The initial temperature of the hot coffee cup is T(0) = 175°F. The cup is placed in a roomtemperature of T... = 70°F. The temperature T(t) of the coffee at time t can be approximated byNewton's law of cooling. ·+hT(t)=hT∞, where h is the convective heat transfer coefficient.dTdt(a) Find the transient solution, Ttran(t).(b) Find the steady-state solution. Tss(t).(c) Determine the total solution T(t).(d) Would increasing the value of h increase or decrease the time when the temperature of coffeereaches the room temp?(e) Would a lower or higher value of h be best for a cup of coffee?

2. The initial temperature of the hot coffee cup is T(0) = 175°F. The cup is placed in a room temperature of T = 70°F. The temperature T(t) of the coffee at time t can be approximated by Newton's law of cooling,+hT(t)=hT, where h is the convective heat transfer coefficient. dt (a) Find the transient solution, Tran(t). (b) Find the steady-state solution, Ts(t). (c) Determine the total solution T(t). (d) Would increasing the value of h increase or decrease the time when the temperature of coffee reaches the room temp? (e) Would a lower or higher value of h be best for a cup of coffee?

2. The initial temperature of the hot coffee cup is T(0) = 175°F. The cup is placed in a room temperature of T = 70°F. The temperature T(t) of the coffee at time t can be approximated by Newton's law of cooling,+hT(t)=hT, where h is the convective heat transfer coefficient. dt (a) Find the transient solution, Tran(t). (b) Find the steady-state solution, Ts(t). (c) Determine the total solution T(t). (d) Would increasing the value of h increase or decrease the time when the temperature of coffee reaches the room temp? (e) Would a lower or higher value of h be best for a cup of coffee?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.3P

See similar textbooks

Related questions

Q: You run the same type of experiment with an unknown mass of silver that began at 75.0˚C and had a…

A: Given data: The specific heat of water is

Q: food product with 85% moisture content is being frozen. Estimate the specific heat of the product at…

Q: 111 moles of water (molar mass 18 g/mole) at 50 °C spontaneously changes temperature. Half of the…

Q: As shown in the figure, a 100 W/m² heat flux is applied to one side of the slab having thickness of…

A: q" = 100 W/m2L = 10 cm = 0.1 mk = 1 W/m.Kh = 10 W/K.m2To find temperature at L = 8 cm = 0.08 m

Q: The initial state of 1.00 mol of a dilute gas is P = 3.00 atm, V = 1.00 L, and Ent 1 = 456 J and its…

Q: Complete the table below by applying the properties of partial derivatives to the internal energy…

A: Given : To find: Complete the table

Q: Two samples of an ideal gas initially at same temperature and pressure are compressed from a volume…

Q: al gas expands adiabatically from a volume of 2.5 x 10- m³ to 3.0 x 10- m. If the initial p

A: given:V1=2.5×10-3m3V2=3×10-3m3p1=5×105paT1=295K

Q: Suppose that as a body cools, the temperature of the surrounding medium increases because it…

A: GivendTdt=kT-Tmk<0Tm=T2+BT1-TB>0

Q: inside it at 900C. What is the equilibrium temperature of the system? Ignore losses to air. Specific…

Q: Derive the work done of an ideal gas undergoing isothermal expansion at temperature T1 if the volume…

A: In an isothermal process temperature remains constant. Consider pressure and volume of ideal gas…

Q: Air (its gas constant is 287 J/kg.k) escapes from a tank at a temperature of 55 C and specific…

A: GIVEN DATA Given that air is the fluid here Gas constant of air = 287 ( J / kg k) Temperature of…

Q: Newton's Law of Cooling says that the rate at which a body cools is proportional to the differnce C…

A: Part A) By apply the initial boundary condition determine the constant value.

Q: Three liquids given the following properties are poured into the cylindrical container with a…

Q: Q2: The temperature of a gas steam is to be measured by a thermocouple. Determine the time it take:…

Q: Q1) A steel cylinder 10 cm in diameter and 10 cm long is initially at 300 °C. It is suddenly…

Q: b) For an Otto Engine the temperature at the end of combustion is 280 K. If the temperature in the…

A: Given Data: The temperature at the end of the combustion is: TG=2800 K. The temperature at the gas…

Q: Question. In a car crash test, a car travelling at a constant speed of 60 km/h collides into a…

A: Given: Mass of the car→m=2150 Kg Spring constant→K=80.98 N/mm Damping constant→C=21.19 N/mm Initial…

Q: In thermodynamics, a distinction is made between functions that are state functions and others that…

A: introduction; state function is also know as point function in thermodynamics. state function define…

Q: A cylinder of cross-section area A is divided into two chambers 1 and 2, by means of a frictionless…

Q: There is a heated continuous stirred tank reactor shown below where the density is constant through…

A: Given Datami-Input mass flowm-output mass flowTi-Inlet TemperatureT-outlet TemperatureEnergy Input-Q…

Q: 5. A 0.350 kg metal ball at an unknown initial temperature is dropped into a Styrofoam cup…

Q: As shown in the diagram, the state of helium gas is changed in such a way that its PV graph is a…

Q: For an ideal gas if the specific internal energy at a specific pressure and temperature of 20 °C is…

A: Given u = 123.8 kJ / kg K

Q: For a certain gas, R=0.277 kJ/kg-K and k=1.384. If 32.55 kJ are transferred to this gas at…

Q: The same engineer decides to look into rates of cooling for liquids to experiment with different…

A: cooling rate equation modelled as, y = 48×0.99×t Where, y= temperature of the Liquid t= time in…

Q: 1000 cm^3 of air at an initial pressure of 1.10 × 10^5 Pa and temperature of 300 K undergoes the…

A: Given: The initial volume of the air, v1 = 1000 cm3 The initial pressure of the air, P1 = 1.1x10^5…

Q: Initial condition: P = 0.7 MPa T = 250oC m = 5 kg Process: Isobaric Final condition: vapor = 3.5 kg…

Q: Five cubic meter of nitrogen are heated at constant volume so that the pressure changes from 276…

Q: ring processing in a steel mill, a 375kg steel casting at 800 degrees is quenched by plunging it…

A: Givenmass of steel casting m=375kgtemperature of steel bath T1=800oCvolume of the oil bath…

Concept explainers

Properties of Pure Substances

A substance with fixed chemical composition throughout is called a pure substance like water, air, and nitrogen. A pure substance does not have to be a single element or compound. A mixture of two or more phases of a pure substance is also a pure substance as long as the chemical composition is the same for all phases. These substances mainly have a constant/ uniform composition. The substances also have fixed boiling and melting points. A pure substance takes part in a chemical reaction to form predictable products.

Question

2. The initial temperature of the hot coffee cup is T(0) = 175°F. The cup is placed in a room
temperature of T... = 70°F. The temperature T(t) of the coffee at time t can be approximated by
Newton's law of cooling. ·+hT(t)=hT∞, where h is the convective heat transfer coefficient.
dT
dt
(a) Find the transient solution, Ttran(t).
(b) Find the steady-state solution. Tss(t).
(c) Determine the total solution T(t).
(d) Would increasing the value of h increase or decrease the time when the temperature of coffee
reaches the room temp?
(e) Would a lower or higher value of h be best for a cup of coffee?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given data

VIEW

Step 2: Sub parts a and b

VIEW

Step 3: sub parts c and d

VIEW

Step 4: sub part e

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Initial condition: P = 0.7 MPaT = 250oCm = 5 kgProcess: IsobaricFinal condition: vapor = 3.5 kgRequired: Heat
6 In a boiler test, the following observations wcre made: 358 A Text Book of Thermal Engineering Feed water temperaturç e= 12" C; Pressure of steam = 11 bar; Dryness fraction of steam 095 Mass of coal burnt 300 kg/h, Calorific value of coal 32 000 kJkg of coal; Mass of water supplied to boiler in 7 hrs 14 min= 14 625 kg. The mass of w ster in the boiler at the end of the test was less than that at the commencement by 900kg. Calculate I. Actual evaporation per kg of coal: 2 Equivalent evaporation from and at 100 C per kg [Ans. 7 15 kg, 8 33 kg: 58.75 % of coal ; and 3. Thermal efficiency of the boiler
A chromel–constantan thermocouple measuring the temperature of a fluid is connected by mistake with copper–constantan extension leads (such that the two constantan wires are connected together and the copper extension lead wire is connected to the chromel thermocouple wire). If the fluid temperature was actually 250 C and the junction between the thermocouple and extension leads was at 90 C, what e.m.f. would be measured at the open ends of the extension leads if the reference junction is maintained at 0 C? What fluid temperature would be deduced from this (assuming that the connection error was not known)?
Classify whether the properties given is for subcooled liquid (SC), saturated liquid (SL), wet mixture (WM), saturated vapor (SsV), superheated vapor (SP) or saturated (S) (can be liquid or vapor) kJ Tsat = 160°C, u = 1000- kg m3 Tsat = 200°C, v = 0.01234 kg Tsat = 200°C, P = 1.5549 MPa 1. Psat = 0.14 MPa,T = 0°C 2. Psat = 1.0 MPa, T = 100°C 7. Peat = 1.4 MPa,T = 150°C kJ Pzat = 0.14 MPa, h = 2000- kg k] Psat = 1.5 MPa, s = 7- kg – K 3. %3D 8. Tsat = 191°C, v = 0.00114291- m3 kg m3 Tsat = 193°C, v = 0.14685 kg 9. 5. 10. sc SL WM sv SP 1 2 3 4 7 8 9 10 6.
complete solution thank you
During processing in a steel mill, a 375kg steel casting at 800 degrees is quenched by plunging it into a 500-gal oil bath, which is initially 75 degrees . After the casting cools and the oil bath warms , what is the final tempertature of the two? The weight per unit volume of the oil is 7.5 lb/gal.
Classify whether the properties given is for subcooled liquid (SC), saturated liquid (SL), wet mixture (WM), saturated vapor (SV), superheated vapor (SP) or saturated (S) (can be liquid or vapor)
The initial state of 1.00 mol of a dilute gas is P1 = 3.00 atm, V1 = 1.00 L, and Eint1 = 456 J and its final state is ?2 = 2.00 atm, V2 = 3.00 L, and Eint 2 = 912 J. The gas is heated and is allowed to expand such that it follows a single straight-line path on a PV diagram from its initial state to its final state. (a) Illustrate this process on a PV diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.
Subject of thermodynamics
A solid hemisphere of radius 5 cm to be cooled in air (at 20 o C, h=10 W/m 2 .K) from 200 oC to center of 150 oC, assume following sphere properties ρ=8500kg/m3, k=20W/m.K , C=400 J/kg.Ka. List assumptions and justify selected method of solution b. How long does it take to cool the hemisphere? c. What is the temperature of the surface at end of cooling?
Conduction 1. A thermodynamic analysis of a proposed Brayton cycle gas turbine yields P= 5 MW of net power production. The compressor, at an average temperature of T. = 400°C, is driven by the turbine at an average temperature of T₁ = 1000°C by way of an L = 1m-long, d= 70mm - diameter shaft of thermal conductivity k = 40 W/m K. Compressor min T Combustion chamber Shaft L Turbine Th out (a) Compare the steady-state conduction rate through the shaft connecting the hot turbine to the warm compressor to the net power predicted by the thermodynamics- based analysis. (b) A research team proposes to scale down the gas turbine of part (a), keeping all dimensions in the same proportions. The team assumes that the same hot and cold temperatures exist as in part (a) and that the net power output of the gas turbine is proportional to the overall volume of the device. Plot the ratio of the conduction through the shaft to the net power output of the turbine over the range 0.005 m s Ls 1 m. Is a…
A cylinder of cross-section area A is divided into two chambers 1 and 2, by means of a frictionless piston. The chambers initially have equal length L. Both chambers are filled with 1 mole of ideal gas, wlth initial pressures M 2Po and Po, respectively. The piston is then allowed to slide freely, whereupon the gas in chamber 1 pushes the piston a distance 1 to equalize the pressure. Consider the following two cases: m (i) The outer walls of the chambers and the piston do not w w mw m allow heat transfer. Denote the distance l as la in this case. (ii) The piston does not allow heat transfer but the chambers are in contact with two heat reservoirs w ww separately, at temperature Tl and T2 for chambers 1 and 2, respectively. Denote the distance 1 as ld in this case. Calculate the ratio la/ld ? Does this ratio have a small or big vala