Thermodynamics ...

One mole of an ideal monatomic gas is taken along the path $$A B C A$$ as shown in the $$P V$$ diagram. The maximum temperature attained by the gas along the path $$B C$$ is given by:

Which of the following integrals depends only on the initial and final states of a thermodynamic system (i.e., independent of the path of transformation)? 

The P-V diagrams of two difference masses $$m_1$$ and $$m_2$$ for an ideal gas at constant temperature $$T$$is given in the figure below.

Some of the thermodynamic parameters are state variables while some are process variables.Some grouping to the parameter are given.Choose the correct one.

A quantity of oxygen $$\left(\lambda=1.4\right)$$ is compressed isothermally until its pressure is doubled. It is then allowed to expand adiabatically until its original volume is restored. The final pressure in terms of initial pressure $${P}_{1}$$ is

10 gm of water is placed in a calorimeter of 100 gm water equivalent at $${10^0}$$. The heat required to raise the temperature of water to $${60^0}{\text{C}}$$ is:-

Two tanks  $$A$$  and  $$B$$  contain water at  $$30 ^ { \circ } \mathrm { C }$$  and  $$80 ^ { \circ } \mathrm { C }$$  respectively. Calculate the amount of water that must be taken from each tank to prepare  $$40\mathrm { kg }$$ water at  $$50 ^ { \circ } \mathrm { C } : -$$

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $$  u=\dfrac{U}{V} \propto T^{4}  $$ and pressure$$ p=\dfrac{1}{3}\left(\dfrac{U}{V}\right) .  $$ If the shell now undergoes an adiabatic expansion the relation between $$  T  $$ and $$  R  $$ is

The specific heat of a substance varies with temperature as $$s = 0.20 + 0.14\theta  + 0.023{\theta ^2}(cal/g{m^ \circ }C)$$. Heat required top raise the temperature of $$2gm$$   of substance from $${5^ \circ }C$$ to $${10^ \circ }$$ is $${\theta}$$ is in $${^ \circ }C$$.

The amount of heat required to raise the temperature of 100gm water from $$20^\circ C$$ to $$40^\circ C$$ will be-