se dp +| dS = se dT Use (ƏS/ƏT), = C,/T and an appropriate Maxwell relation to show that TdS = C,dT- aTVdp, where the expansion coefficient, a, is defined as a= (1/V)(av/ƏT),. Hence, show that the energy transferred as heat, q, when the pressure on an incompressible liquid or solid is increased by Ap in a reversible isothermal process is given by q = -aTVAp. Evaluate q when the pressure acting on 100 cm' of mercury at 0°C is increased by 1.0 kbar. (a= 1.82 × 10*K'.) P3E.6 Suppose that S is regarded as a function of p and T so that

se dp +| dS = se dT Use (ƏS/ƏT), = C,/T and an appropriate Maxwell relation to show that TdS = C,dT- aTVdp, where the expansion coefficient, a, is defined as a= (1/V)(av/ƏT),. Hence, show that the energy transferred as heat, q, when the pressure on an incompressible liquid or solid is increased by Ap in a reversible isothermal process is given by q = -aTVAp. Evaluate q when the pressure acting on 100 cm' of mercury at 0°C is increased by 1.0 kbar. (a= 1.82 × 10*K'.) P3E.6 Suppose that S is regarded as a function of p and T so that

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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(a) Calculate the final temperature of a sample of CO2 of mass 16.0 g that is expanded reversibly and adiabatically from 500 cm at 298.15 K to 2. 00 dm³ if Cp.m is equal to 37.11 J K' mol'. Tr=Ti (Vi/Vr)"C
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(a) For an ideal gas equation of state, prove that P P P dP = dn +=dT dv n (b) Suppose 1.000 mol of ideal gas at 300.0 K in a 30.00 L vessel increased in volume by 0.050 L. Use your answer from part (a) to compute the change in the pressure AP. (c) Compare to the exact change in pressure using the ideal gas equation of state to the estimate given by AP.
1) One mole of an ideal monoatomic gas is the working substance of a thermal machine that operates according to the cycle in the figure: State 1 has pressure P=2,68 atm, volume V= 4,37 m^3 and temperature T=175 K. Pressure P' is 5 times greater than P and volume V' is 5 times greater than V.a) What are the temperatures of states 2, 3 and 4?b) What is the work, in joules, done by the gas during the cycle?c) What is the energy supplied to the gas, in joules, as heat during the cycle?d) What is the efficiency, in percentage, of this thermal machine?
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3. Derive the thermodynamic equation of state for an ideal gas starting from internal energy then express this equation in a form without differentials. = -P +T| T LƏT.
13. (a) How much heat wiH be evolved or absorbed in the solution of 2 moles of H,SO,(1) in a very large volume of water at 25°C? (b) What will be the dif- ferential heats of solution of the acid and the water under these conditions?
Suppose a piece of solid lead weighing 41.3 g at a temperature of 312 °C is placed in 413 g of liquid lead at a temperature of 374 °C. Calculate the temperature after thermal equilibrium is reached, assuming no heat loss to the surroundings. The enthalpy of fusion of solid lead is AH fus = 4.77 kj mol¹ at its melting point of 328 °C, and the molar heat capacities cp of solid and liquid lead are 26.9 and 28.6 J K¹ mol-¹, respectively. (Enter your answer to three significant figures.) T₁= Jc Submit Answer Try Another Version 1 item attempt remaining
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(b) An ideal gas of 2.5 moles undergoes an adiabatic expansion at an initial pressure of 4.25 bar and at an initial temperature of 540 K to a final temperature of 400 K. Calculate the work done which is equal to internal energy change under such conditions. Assume Cp,m = 5/2 R %3D