Chapter 1.2, Problem 10R

To determine

To convert: the units.

Answer to Problem 10R

The required time is the converted temperature is $\boxed{T_K=300.15\text{ K}}$ , mass is $\boxed{m=0.002\text{ kg}}$ and length is $\boxed{l=30\text{ dm}}$ .

Explanation of Solution

Given:

Temperature is T⁰ = 27⁰C.

Mass is m = 20 dg.

Length is l = 3 m.

Formula used:

The conversion of temperature from degree Celsius to Kelvin is,

  $T_K=T^0+273.15$....................(1)

Here, T_k is the temperature in Kelvin and T⁰ is the temperature in degree Celsius.

The conversion of mass from decigram to kilogram is,

  $1\text{ dg = }\frac{1}{10000}\text{kg}$....................(2)

The conversion of length from meter to decimeter is,

  $1\text{ m = }10\text{ dm}$ ....................(3)

Calculation:

Substitute 27⁰ C for T⁰ in equation (1)

  $\begin{array}{l}{T}_K={27}^0+273.15\\ \boxed{T_K=300.15\text{ K}}\end{array}$

Multiply 20 dg for m with 1/10000kg in equation (2)

  $\begin{array}{l}m=20\times \frac{1}{10000}\\ \boxed{m=0.002\text{ kg}}\end{array}$

Multiply 3m for l with 10dm in equation (3)

  $\begin{array}{l}l=3\times 10\\ \boxed{l=30\text{ dm}}\end{array}$

Conclusion:

Hence, the converted temperature is $\boxed{T_K=300.15\text{ K}}$ , mass is $\boxed{m=0.002\text{ kg}}$ and length is $\boxed{l=30\text{ dm}}$ .