Question

An ideal monoatomic gas at temperature ${27}^{\circ }\text{C}$ and pressure ${10}^6{\text{N/m}}^2$ occupies $10\text{L}$ volume. $10,000\text{cal}$ of heat is added to the system without changing the volume. Calculate the change in temperature of the gas. Given:$R=8.31\text{J/mol-K}$ and $J=4.18\text{J/cal}$

• A. $500\text{K}$
• B. $833\text{K}$
• C. $300\text{K}$
• D. $0\text{K}$

Answer 1

The correct option is B $833\text{K}$

For $n$ moles of gas, we have $PV=nRT$
Here, $P={10}^6{\text{N/m}}^2,V={10}^{-2}{\text{m}}^3$
and $T={27}^{\circ }\text{C}=300\text{K}$
$\therefore n=\frac{PV}{RT}=\frac{{10}^6\times {10}^{-2}}{8.31\times 300}=4.0$

For monoatomic gas, $C_V=\frac{3}{2}R$
Thus, $C_V=\frac{3}{2}\times 8.31\text{J/mol-K}$
$=\frac{3}{2}\times \frac{8.31}{4.18}\approx 3\text{cal/mol-K}$
Let $\Delta T$ be the rise in temperature when $n$ moles of the gas is given $Q\text{cal}$ of heat at constant volume. Then,
$Q=n{C}_V\Delta T$ or $\Delta T=\frac{Q}{n{C}_V}$
$=\frac{10000\text{cal}}{4.0\text{mole}\times 3\text{cal/mol-K}}$
$\approx 833\text{K}$