Thermodynamics ...

$$N$$ moles of a monoatomic gas is carried round the reversible rectangular cycle $$ABCDA$$ as shown in the diagram. The temperature at $$A$$ is $${T}_{0}$$. The thermodynamic efficiency of the cycle is:

The relation between internal energy U, pressure P and Volume V of a gas in an adiabatic process is $$U=a+bPV$$, where a and b are positive constants. What is the value of $$\gamma$$

The relation between internal energy U, pressure P and volume V of a gas in an adiabatic process is U=a+bPV, where a and b are positive constants. What is the value of $$\gamma$$?

A monoatomic ideal gas at temperature $$T_{1}$$, is enclosed in a cylinder with a frictionless piston. The gas is allowed to expanded adiabatically to a temperature $$T_{2}$$ by releasing the piston suddenly. If $$L_{1}$$, and $$L_{2}$$ are lengths of the gas columns before and after expansion respectively, then $$\frac{T_{1}}{T_{2}}$$ is given by:

In a thermodynamic process pressure of a fixed mass of a gas is changed in such a manner that the gas releases $$20J$$ of heat and $$8J$$ of work is done on the gas. If initial internal energy of the gas was $$30J$$, what will be the fixed internal energy?

A ring shaped tube contains two ideal gases with equal masses and molar masses $$M_1=32$$ and $$M_2=28$$. The gases are separates by one fixed partition and another movable stopper $$S$$ which can move freely without friction inside the ring. The angle $$\alpha$$ as shown in the figure is _________ degrees.

Three samples of the same gas A, B and C$$\left( \gamma =3/2 \right) $$ have equal volume initially. Now, the volume of each sample is doubled. For A, the process is adiabatic; for B, it is isobaric and for C, the process is isothermal. If the final pressures are equal for all the three samples, the ratio of their initial pressures is

A fixed thermally conducting cylinder has a radius R and height $$L_0$$. The cylinder is open at its bottom and has a small hole at its top. A piston of mass M is held at a distance L from the top surface, as shown in the figure. The atmospheric pressure is $$P_0$$.
While the piston is at a distance $$2L$$ from the top, the hole at the top is sealed. The piston is then released, to a position where it can stay in equilibrium. In this condition, the distance of the piston from the top is?

When an ideal monoatomic gas is heated at constant pressure, the fraction of the heat energy supplied which increases the internal energy of the gas is

The characterisic distance at which quantum gravitational effects are significant, the Planck length, can be determined from suitable combination of the fundamental physical constants $$G$$. $$h$$ and $$c$$. Which of the following correctly gives the Planck length?