Show that the adiabatic curve is steeper than the isothermal curve.

An ideal gas (1 mol ,monatomic) is in the initial state P (see diagram) on an isothermal curve A at a temperature T_0 . It is brought under a constant volume (2V_0) process to Q which lies on an adiabatic curve B intersecting the isothermal curve A at (P_0,V_0,T_0) . The change in the internal energy of the gas (in terms of T_0 ) during the process is (2^(2//3)=1.587)

Statement-1: Temperature of a system can be increased without supplying heat. Statement-2: If the initial volume of system is equal to final volume in a process then work done is necessarily zero. Statement-3: If an adiabatic curve for a gas intersect with an isothermal curve for the same gas then at the point of intersection, the ratio of slope of the adiabatic and the isothermal curve is gamma .

Show that the slope of adiabatic curve at any point is Yama times the slope of an isothermal curve at the corresponding point.

State true or false. Work done by an ideal gas in adiabatic expansion is less than that in isothermal process (for same temperature range)

Show that the slope of p-V diagram is greater for an adiabatic process as compared to an isothermal process.

A sphere is inscribed in a cylinder such that spere touches the cylinder . Show that the curved surface of spere is equal to the curved surface of cylinder.

The curves A and B in the figure shown P-V graphs for an isothermal and an adiabatic process for an idea gas. The isothermal process is represented by the curve A.

The curves A and B in the figure shown P-V graphs for an isothermal and an adiabatic process for an idea gas. The isothermal process is represented by the curve A.

For a p-V plot, the slope of an adiabatic curve = x × slope of isothermal at the same point. Here x is :

Show that there is no cubic curve for which the tangent lines at two distinct points coincide.