- #1
A13235378
- 50
- 10
- Homework Statement
- Consider an Otto Cycle:
1-->2 (adiabatic)
2-->3 (isochoric)
3-->4 (adiabatic)
4-->1 (isochoric)
Knowing that:
P1 = 10^5 Pa
V1= 0,8 m^3
T1 = 290K
V3= 0,1m^3
cv= 0,171 Kcal/kg . K
Gas mass = 1 kg
gamma (coefficient of adiabatic expansion) = 1,4
V1=V4
V2=V3
Q23 = heat received
Q41 = heat expelled
Find T2,T3,T4 and P2,P3,P4
- Relevant Equations
- pv/t = constant
p(v)^gamma= constant
t v^(1-gamma) = constant
Q = m. cv . (T'-T)
1-->2 (adiabatic)
$$P_1V_1^γ=P_2V_2^γ$$
$$P_2=18,4.10^5Pa$$
$$T_1V_1^{1-\gamma}=T_2V_2^{1-\gamma}$$
$$T_2=429,32K$$
2-->3 (isochoric)
$$\frac{P_2}{T_2}=\frac{P_3}{T_3}$$
$$\frac{18,4.10^5}{429,32}=\frac{P_3}{T_3}$$
3--> 4 (adiabatic)
$$P_3V_3^{\gamma}=P_4V_4^{\gamma}$$
$$T_3V_3^{\gamma-1}=T_4V_4^{\gamma-1}$$
4--> 1 (isochoric)
$$\frac{P_1}{T_1}=\frac{P_4}{T_4}$$
From here, I can no longer find the values of P3, P4, T3, T4, as it is as if each equation is an association of the other. So I was wondering if there is a way to resolve this issue, because for me, I believe that data is missing.
$$P_1V_1^γ=P_2V_2^γ$$
$$P_2=18,4.10^5Pa$$
$$T_1V_1^{1-\gamma}=T_2V_2^{1-\gamma}$$
$$T_2=429,32K$$
2-->3 (isochoric)
$$\frac{P_2}{T_2}=\frac{P_3}{T_3}$$
$$\frac{18,4.10^5}{429,32}=\frac{P_3}{T_3}$$
3--> 4 (adiabatic)
$$P_3V_3^{\gamma}=P_4V_4^{\gamma}$$
$$T_3V_3^{\gamma-1}=T_4V_4^{\gamma-1}$$
4--> 1 (isochoric)
$$\frac{P_1}{T_1}=\frac{P_4}{T_4}$$
From here, I can no longer find the values of P3, P4, T3, T4, as it is as if each equation is an association of the other. So I was wondering if there is a way to resolve this issue, because for me, I believe that data is missing.
