The specific heat of argon at constant volume is 0.3122kj/kg k. Find the specific heat of argon at constant pressure if R = 8.314kj/kmol k. (molecular weight of argon is 39.95).(A) 520.3(B) 530.2(C) 230.5(D) 302.5

Given Data:
• Specific heat of argon at constant volume CV=0.3122 kJ/kg KC_V = 0.3122 \, \text{kJ/kg K}
• Universal gas constant R=8.314 kJ/kmol KR = 8.314 \, \text{kJ/kmol K}
• Molecular weight of argon M=39.95 g/molM = 39.95 \, \text{g/mol}
• We need to find the specific heat of argon at constant pressure CPC_P.
Relation between CPC_P and CVC_V:
For an ideal gas, the relationship between the specific heat at constant pressure CPC_P and the specific heat at constant volume CVC_V is given by:
CP=CV+RC_P = C_V + R
However, RR in this equation must be expressed in units of kJ/kg K\text{kJ/kg K} because CPC_P and CVC_V are given in kJ/kg K\text{kJ/kg K}.
Converting the Universal Gas Constant to Specific Units:
The universal gas constant RR is given in terms of kJ/kmol K\text{kJ/kmol K}, but we need it in kJ/kg K\text{kJ/kg K}. To convert RR to the desired units, we use the molecular weight MM of argon:
Rspecific=RM=8.314 kJ/kmol K39.95 kg/kmol=0.208 kJ/kg KR_{\text{specific}} = \frac{R}{M} = \frac{8.314 \, \text{kJ/kmol K}}{39.95 \, \text{kg/kmol}} = 0.208 \, \text{kJ/kg K}
Now, we can calculate CPC_P:
CP=CV+Rspecific=0.3122 kJ/kg K+0.208 kJ/kg K=0.5202 kJ/kg KC_P = C_V + R_{\text{specific}} = 0.3122 \, \text{kJ/kg K} + 0.208 \, \text{kJ/kg K} = 0.5202 \, \text{kJ/kg K}
Thus, the specific heat of argon at constant pressure CPC_P is approximately 520.3 kJ/kg K.
A) 520.3\boxed{\text{A) 520.3}}