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A system goes from $A$ to $B$ via two processes $I$ and $II$ as shown in figure. If $\Delta {U_1}$ and $\Delta {U_2}$ are the changes in internal energies in the processes $I$ and $II$ respectively, then
If $\Delta Q$ and $\Delta W$ represent the heat supplied to the system and the work done on the system respectively, then the first law of thermodynamics can be written as
Initial pressure and volume of a gas are $ P$ and $V$ respectively. First it is expanded isothermally to volume $4V$ and then compressed adiabatically to volume $ V$. The final pressure of gas will be
Two carnot engines $A$ and $B$ operate in series such that engine $A$ absorbs heat at $T_{1}$ and rejects heat to a sink at temperature $T$. Engine $B$ absorbs half of the heat rejected by engine $A$ and rejects heat to the sink at ${T}_{3}$. When workdone in both the cases is equal, the value of ${T}$ is
A gas ($\gamma = 1.3)$ is enclosed in an insulated vessel fitted with insulating piston at a pressure of ${10^5}\,N/{m^2}$. On suddenly pressing the piston the volume is reduced to half the initial volume. The final pressure of the gas is
The pressure in the tyre of a car is four times the atmospheric pressure at $300 K$. If this tyre suddenly bursts, its new temperature will be $(\gamma = 1.4)$
A sample of an ideal gas is taken through the cyclic process $abca$ as shown in the figure. The change in the internal energy of the gas along the path $ca$ is $-180\, J$. The gas absorbs $250\, J$ of heat along the path $ab$ and $60\, J$ along the path $bc$. The work done by the gas along the path $abc$ is ..... $J$
The three processes in a thermodynamic cycle shown in the figure are : Process $1 \rightarrow 2$ is isothermal; Process $2 \rightarrow 3$ is isochoric (volume remains constant); Process $3 \rightarrow 1$ is adiabatic. The total work done by the ideal gas in this cycle is $10 \,J$. The internal energy decreases by $20 \,J$ in the isochoric process. The work done by the gas in the adiabatic process is $-20 \,J$. The heat added to the system in the isothermal process is .............. $J$
A Carnot engine has efficiency of $50 \%$. If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$. The temperature of the source will be$....K$