Question

Question 5 (2.0 pts) Assume that Cp for an ideal gas is given by co(T) = 0.9 + 2.5 x 10-* T, in kJ/kg-K, where is the temperature in Kelvin. (Use the gas constant R = 0.3 kJ/kg-K) (a) (+0.4) Derive an expression for Cy as a function of temperature. The gas undergoes an isochoric process from a temperature T, = 400 K to T2 = 500 K. Calculate the change in (b) (+0.6) enthalpy, in kJ/kg, (c) (+0.6) entropy, in kJ/kg-K, and (d) (+0.4) internal energy, in kJ/kg.

Answer 1

Solution:

Isochoric process is also called as constant volume process.In constant volume process workdone is zero.so,according to first law of thermodynamics,heat transfer will be equal to change in internal energy.(Q=$\Delta$U).

GIVEN DATA : Cp (T) = 0.9 +2.5*10*7 , in kJ kg.k R=0.3 KJ kg.k Solution: The gas undergoes an Isochoric process from a temperature TI = 400K to Tg = 500k @ ev as a function of temperature. we know that, - we know, . (p = 0.9 +2.5x10tr , in kg Kyok (0.9 +2:5 x164T) - R = CV cv = (0.9+2.5X164T) -0.3 Pov = 0.6 +2.5x1077), in KI & Answer home Kock

(b) Enthalpy, in kJ 72 DH = 16. dt is formula. 500 | (0.9 +2.5x1047) .dt = [0.25 +2.52102 =[6.44560 + 25 205 * 50g] – (0.94480 +8 526*s ace) = 481.25 - 380 for understanding para 101-25 tahun mere DH = 101.25 [ St-dt = To mamma where, īst. AH= Change in entropy.

(C) entropy, in KI kg.k We know, first law of Thermodynamics is. Qing out wi-2 ->U) divide 0) by T orm where, we know, for isochoric process Wi-2 = p (V2 - 11)=0 W1-2 = work done during process =0 As = change in entropy to ASE 416 AS = é -112 Du = cr. dT (Cv specific heat at constant volume) As = helt cr. dt 1 a tomula.

500 = 16.6 +2.5x1045), TT - - - 500 (946 + 25206T .47 400 for understanding 500 Coob + 2.5810*) .dt It.dt= int 900 500 = [ows + 2 5 20*) =[0.6 XIN 500 + 2.5 X164 x 1500] - [0.6 mln 400 + 2.5 x604x4007 = [5.853] -[3.694] AS = o.159 KJ 0 = 0159 revent Answer kg.k

(d) change in internal energy. Du= co.dt a formula Ti (6.6 +2.5x1097) .IT 500 (0.8+ 2.581047) odt 500 - Forst +2.5**) = [0.62500 + 25xwi ye? ] - [uox 400 + 25 +10% acred] = 331.25 - 260 10 = 71.25 KJ Ацил -- m