Chapter 13, Problem 18A

Interpretation Introduction

Interpretation:

The temperature at two different conditions have to be calculated.

Concept Introduction:

Charles’s law: The volume of a given amount of gas is proportional to its temperature (in K) of the gas at constant pressure.

The relationship between volume of a gas and temperature is expressed as-

  $\begin{array}{l}V\propto T\\ \mathrm{or},\frac{V}{T}=Constant\end{array}$ When P is constant.

Charles’s law can also be expressed in mathematical form as-

  $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

In the above equation, V₁ is initial volume and T₁ is initial temperature, while V₂ is final or new volume and T₂ is final or new temperature.

Answer to Problem 18A

1. The temperature is -123.9 °C.
2. The temperature is 323.4 °C.

Explanation of Solution

Data given: V₁ =266 L

T₁ = 25.2 °C = (273 + 25.2) K = 298.2 K

Case I: Volume is reduced to its half means-

  ${\mathrm{V}}_2=\frac{V_1}{2}or,\frac{V_2}{V_1}=\frac{1}{2}$

  $\begin{array}{l}\frac{V_1}{T_1}=\frac{V_2}{T_2}\\ T_2=\left(\frac{V_2}{V_1}\right)\times T_1=\frac{1}{2}\times 298.2K\\ =149.1K=-123.9°C\end{array}$

Case II: Volume of the neon sample is doubled means-

  ${\mathrm{V}}_2=2V_{1}or,\frac{V_2}{V_1}=2$

  $\begin{array}{l}\frac{V_1}{T_1}=\frac{V_2}{T_2}\\ T_2=\left(\frac{V_2}{V_1}\right)\times T_1=2\times 298.2K\\ =596.4K=323.4°C\end{array}$