When an ideal diatomic gas is heated at constant pressure then what fraction of heat given is used to increase internal energy of gas?
If it is heated at constant pressure, the volume must increase
heat in = change in internal energy + work out
dQ = dU + dW
P V = n R T
constant pressure
P dV = n R dT = work out
Change in internal energy = n Cv dT = n(5/2)R dT for diatomic gas
total heat required = n R dT + (5/2)n R dT
so our answer is (5/2) / (1+5/2)
= 5/(2+5) = 5/7
To determine the fraction of heat given that is used to increase the internal energy of an ideal diatomic gas when heated at constant pressure, we need to understand the concept of specific heat capacities.
Specific heat capacity is defined as the amount of heat required to raise the temperature of a given amount of substance by a specific amount. For gases, there are two specific heat capacities: specific heat capacity at constant pressure (Cp) and specific heat capacity at constant volume (Cv).
In this case, since the gas is being heated at constant pressure, we are concerned with the specific heat capacity at constant pressure (Cp). The heat given to the gas is equal to the product of the specific heat capacity at constant pressure (Cp), the change in temperature (ΔT), and the number of moles of gas (n).
Heat given (Q) = Cp * ΔT * n
The change in internal energy (ΔU) of a gas is related to the heat given (Q) by the following equation:
ΔU = Q - W
Where ΔU is the change in internal energy, Q is the heat given to the gas, and W is the work done by the gas.
At constant pressure, the work done by the gas is given by:
W = P * ΔV
With ΔV being the change in volume and P being the pressure.
Since the internal energy (ΔU) only depends on the temperature change (ΔT), we can write:
ΔU = Cp * ΔT * n - P * ΔV
However, for an ideal gas, the change in internal energy (ΔU) depends only on the temperature change (ΔT) and the number of moles of the gas (n), and is independent of pressure and volume changes. This is because ideal gases do not experience intermolecular forces or significant volume changes at low pressures.
Therefore, in this case, when an ideal diatomic gas is heated at constant pressure, all the heat given (Q) is used to increase the internal energy (ΔU) of the gas.
In conclusion, when an ideal diatomic gas is heated at constant pressure, the fraction of heat given that is used to increase the internal energy of the gas is 100%.