Question

1/2 mole of Helium gas is contained at S.T.P. The heat energy needed in cal to double the pressure of the gas, keeping the volume constant

• A. $3276J$
• B. $1638J$
• C. $819J$
• D. $409.5J$

Answer 1

The correct option is B $1638J$

Let $P_1$ and $P_2$ be the initial pressure and final pressure respectively. $T_1$ and $T_2$ be the initial and final temperature respectively.

Given,

Number of moles, $n-\frac{1}{2}$

$P_2=2P$

$P_1=P$

$T_1=273K$

We have the equation,

$\frac{P_2}{T_2}=\frac{P_1}{T_1}$

or

$\frac{2P}{T_2}=\frac{P}{273}$

$T_2=546k$

Change in temperature, $dT=T_2-T_1=273K$

Again,

$dQ=n{C}_{v}dT$

$=\frac{1}{2}\times 4\times 3\times 273=1638J$