Final answer:
The energy required to heat a fixed mass of an ideal gas from 50 to 80°C is the same for both 1 atm and 3 atm pressure, as it depends on the temperature change, not the pressure for an ideal gas.
Step-by-step explanation:
The question asks about the energy required to heat a fixed mass of an ideal gas from 50 to 80°C at two different constant pressures. In general, the energy required to heat a gas at constant pressure is related to its change in temperature and the amount of gas. However, at constant pressure and for the same mass and type of gas, the amount of energy required solely depends on the temperature change, not the pressure, due to the molar heat capacity at constant pressure (Cp) being a function of temperature only for an ideal gas.
In both cases (a) 1 atm and (b) 3 atm, since the temperature change is the same and the ideal gas law assumes no interactions between the particles, the energy required should theoretically be equal. Hence, whether the gas is under 1 atm or 3 atm pressure, the energy required will be the same to achieve the same temperature rise.