Is the relation DeltaU mCvDelta t restricted to constantvol

Is the relation DeltaU = mC_vDelta t restricted to constant-volume processes only or can it be used for any kind of process of an ideal gas? (b) Is the energy required to heat air from 295 to 305 K the same as the energy required to heat it from 345 to 355 K? Assume the pressure remains constant in both cases. (c) A fixed mass of an ideal gas is heated from 50 to 80degree C at a constant pressure of (a) 1 atm and (b) 3 atm. For which case do you think the energy required will be greater? (d) Is it possible to compress an ideal gas isothermally in an adiabatic piston-cylinder device?

Solution

b) Energy requried to heat air from 295 to 305 K is equal to energy required to heat if from 345 to 355 because here tempreture differece is same, and pressure remains constant mCp(T2-T1) is same for both condtions.

a) this relation is used for constant volume process only because here volume is constant.

c) at 1 atm pressure the energy required will be greater because for pressure decreasing with increasing altitude. At mountain peaks pressure is low , for cooking more energy is required. so energy is required is increasing with decreasing pressure.

d) not possible, if we compress the ideal gas the pressure will change which directly effects the temperature.