Question

Piston cylinder device initially contains $0.5m^3$ of nitrogen gas at $400kPa$ and ${27}^o$C. An electric heater within the device is at 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.
$R=\frac{25}{3}kJ/kmol-K$

The final temperature of nitrogen is:

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

Answer 1

Answer: (B)

${56.6}^{o}C$

Heat supplied to the gas by the heater $H=120\times 2\times (5\times 60)=72kJ$
Heat lost: $H_{lost}=2800J=2.8kJ$
mass of nitrogen $m=\frac{P_1{V}_1}{R{T}_1}=\frac{400kPa\times 0.5m^3}{0.297kPa{m}^{3}k{g}^{-1}{K}^{-1}}\times (27+273)K=2.245kg$ where $R=0.297kPa{m}^{3}k{g}^{-1}{K}^{-1}$

Work done by the gas at constant Pressure $W=H-H_{lost}=72-2.8=69.2J$
$\therefore m{C}_p(T_2-300)=69.2$
$\therefore 2.245\times 1.039(T_2-300)=69.2$
$\therefore T_2={56.7}^{o}C$