A Carnot engine operates between two reservoirs of temperatures $900\; \mathrm{K}$ and $300 \;\mathrm{K}$ The engine performs $1200\; \mathrm{J}$ of work per cycle. The heat energy (in $\mathrm{J}$ ) delivered by the engine to the low temperature reservoir, in a cycle. is
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In the $p-V$ diagram below, the dashed curved line is an adiabat.For a process that is described by a straight line joining two points $X$ and $Y$ on the adiabat (solid line in the diagram) heat is (Hint consider the variation in temperature from $X$ to $Y$ along the straight line)
A gas mixture consists of $8$ moles of argon and $6$ moles of oxygen at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of $\frac{{{C_P}}}{{{C_V}}}$ for the gas is
This question has Statement $1$ and Statement $2.$ Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement $1:$ In an adiabatic process, change in internal energy of a gas is equal to work done on/by the gas in the process.
Statement $2 :$ The temperature of a gas remains constant in an adiabatic process.
In $1^{\text {st }}$ case, Carnot engine operates between temperatures $300\,K$ and $100\,K$. In $2^{\text {nd }}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $2^{\text {ad }}$ case) will be.
One mole of an ideal gas $(\gamma = 1.4)$ is adiabatically compressed so that its temperature rises from $27\,^oC$ to $35\,^oC$ . The change in the internal energy of the gas is .... $J$. (given $R = 8.3\,J/mole-K$ )
An ideal Carnot engine, whose efficiency is $40 \%$ receives heat at $500\; K$. If its efficiency is $50 \%$ then the intake temperature for the same exhaust temperature is ......... $K$
When an ideal gas in a cylinder was compressed isothermally by a piston, the work done on the gas was found to be $1.5 \times {10^4}\;joules$. During this process about
$n$ moles of a van der Waals' gas obeying the equation of state $\left(p+\frac{n^2 a}{V^2}\right)(V-n b)=n R T$, where $a$ and $b$ are gas dependent constants, is made to undergo a cyclic process that is depicted by a rectangle in the $p-V$ diagram as shown below. What is the heat absorbed by the gas in one cycle?