Question

Piston cylinder device initially contains $0.5m^3$ of nitrogen gas at $400kPa$ and ${27}^{\circ }C$. An electric heater within the device is turned on and is allowed to pass a current of $2A$ for $5min$ from a $120V$ source. Nitrogen expands at constant pressure and a heat loss of $2800J$ occurs during the process. $R=\frac{25}{3}kJ/kmolK$ . The final temperature of nitrogen is

• A. ${2.6}^{\circ }C$
• B. ${56.6}^{\circ }C$
• C. ${29.6}^{\circ }C$
• D. ${5.67}^{\circ }C$

Answer 1

Answer: (B)

${56.6}^{\circ }C$

Gas is nitrogen hence diatomic$\Rightarrow C_p=7/2R$
Given initial temperature $=T_0=300K$, Initial pressure $=P_0=400kPa$, Initial volume=$V_0=0.5m^3$
Applying ideal gas equation, number of moles, $n=P_0{V}_0/RT=\frac{400\times 0.5}{25/3\times 300}=.08kmol=80mol$
Heat supplied $=2\times 5\times 60\times 120=72000J=72kJ$
Also heat released $=2.8kJ$
Net heat absorbed = heat supplied-heat released $=n{C}_p\Delta T=69200\Rightarrow 80\times 7/2\times 25/3\times \Delta T=69200$
$\Rightarrow \Delta T=29.6K\Rightarrow T=329.6K$
Hence, final temperature is 56.6 degrees.