# GATE2015-1-54

A well insulated rigid container of volume $1 \: m^3$ contains $1.0 \: kg$ of an ideal gas $[C_p = 1000 \: J/(kg\cdot K)$ and $C_v=800 J/(kg \cdot K)]$ at a pressure of $105 \: Pa$. A stirrer is rotated at constant rpm in the container for $1000$ rotations and the applied torque is $100 \: N-m$. The final temperature of the gas (in $K$) is

1. $500.0$
2. $773.0$
3. $785.4$
4. $1285.4$

recategorized

## Related questions

In a $3$-stage air compressor, the inlet pressure is $p_1$, discharge pressure is $p_4$.and the intermediate pressures are $p_2$ and $p_3 ( p_2 < p_3)$. The total pressure ratio of the compressor is $10$ and the pressure ratios of the stages are equal. If $p_1 = 100$ $kPa$, the value of the pressure $p_3$ (in $kPa$) is __________
Steam enters a well insulated turbine and expands isentropically throughout. At an intermediate pressure, $20$ percent of the mass is extracted for process heating and the remaining steam expands isentropically to $9 \: kPa$ ... $100$ $kg/s$, then the work output (in $MW$) is _________
A stream of moist air (mass flow rate $= 10.1 \: kg/s$) with humidity ratio of $0.01 \: \dfrac{kg}{\text{kg dry air}}$ mixes with a second stream of superheated water vapour flowing at $0.1 \: \text{kg/s}$. Assuming proper and uniform mixing with no condensation, the humidity ratio of the final stream $\big($in $\dfrac{kg}{\text{kg dry air}} \big )$ is _____________
Air enters a diesel engine with a density of $1.0$ $kg$/$m^3$. The compression ratio is $21$. At steady state, the air intake is $30 × 10^{-3}$ $kg/s$ and the net work output is $15$ $kW$. The mean effective pressure (in $kPa$) is ____________
A Carnot engine ($CE_1$) works between two temperature reservoirs $A$ and $B$, where $T_A$ = $900$ $K$ and $T_B$ = $500$ $K$. A second Carnot engine ($CE_2$) works between temperature reservoirs $B$ and $C$, where $T_C$ = $300$ $K$. In each cycle of $CE_1$ and ... $Q$ absorbed by $CE_1$ from reservoir $A$ is $150$ $MJ$, the net heat rejected to reservoir $C$ by $CE_2$ (in $MJ$) is ______________