Specific Heat Capacities - Gases

Can a process on an ideal gas be both adiabatic and isothermal?

Can we define specific heat capacity for an adiabatic process?

5 g of a gas is contained in a rigid container and is heated from 15°C to 25°C. Specific heat capacity of the gas at constant volume is 0.172 cal g⁻¹ °C⁻¹ and the mechanical equivalent of heat is 4.2 J cal⁻¹. Calculate the change in the internal energy of the gas

The specific heat capacity of water is 

An engine takes in 5 moles of air at 20°C and 1 atm, and compresses it adiabatically to `1/10^"th"` of the original volume. Assuming air to be a diatomic ideal gas made up of rigid molecules, the change in its internal energy during this process comes out to be X kJ. The value of X to the nearest integer is ______.

The figure shows two vessels with adiabatic walls, one containing 0.1 g of helium (γ = 1.67, M = 4 g mol⁻¹)  and the other containing some amount of hydrogen (γ = 1.4, M = 2 g mol⁻¹). Initially, the temperatures of the two gases are equal. The gases are electrically heated for some time during which equal amounts of heat are given to the two gases. It is found that the temperatures rise through the same amount in the two vessels. Calculate the mass of hydrogen.