Question

An ideal monoatomic gas at temperature ${27}^{\circ }\text{C}$ and pressure $100\text{bar}$ occupies $5\text{L}$ volume. $5000\text{cal}$ of heat is added to the system without changing the volume. Calculate the change in temperature of the gas. (Given, $R=8.31\text{J/mol K}$)

• A. $75\text{K}$
• B. $89\text{K}$
• C. $83\text{K}$
• D. $90\text{K}$

Answer 1

The correct option is C $83\text{K}$

From Ideal gas equation,
$PV=nRT$
$\Rightarrow n=\frac{PV}{RT}$
$=\frac{{10}^7\times 5\times {10}^{-3}}{8.31\times 300}$
[from the data given in the question]
$\Rightarrow n=0.2\times 100=20$

For monoatomic gas,
$C_V=\frac{3}{2}R$
$=\frac{3}{2}\times 8.31\text{J/mol-K}$
$=\frac{3}{2}\times \frac{8.31}{4.18}\approx 3\text{cal/mol K}$
Let $\Delta T$ be the rise in temperature
So $Q=n{C}_V\Delta T$
$\Rightarrow \Delta T=\frac{Q}{n{C}_V}$
$=\frac{5000}{20\times 3}=83.33$
$\approx 83\text{K}$