Question

of gas ind R that ? Tp yap 1. Consider the following piston-cylinder arrangement which is thermally insulated. Initially, the same 1 mole of ideal gas are confined in the cylinder A, B and C, respectively which are partitioned by a adiabatic piston and a diathermic piston as shown in Figure 1. The initial volume and absolute temperature (K) of three partitions are the same as V, and to respectively and the pressure of the cylinder is given by P, as shown in Figure 1. When heat (a) was gradually supplied to A, the gas of A was reversibly expanded until the volume of C cylinder is + V, and it was then reached at the final equilibrium as shown in Figure 2. (Suppose that the molar heat capacity is C = 2R. In addition, assume that the friction between the cylinder and the piston and the mass of the piston are ignored. The heat capacity of a diathermic piston is also ignored.) Thermally Folklor - insulated Adiabatic piston cylinder as is the 194 방의 온도는 that ated e of Adiabatic piston PONOTO of -v C Figure 1 Figure 2 Diathermic piston 여들에 가름 불가능 P.Vo the end Calculate the value of - Testy znal Eq.

Answer 1

From figure 2

The amount of heat supply is equal to change in heat of the system. Now your all system is insulated means no direct heat transfer from surrounding. Between cylinder A and B adiabatic piston means no heat transferring in B, between B and C diathermic wall means B and C. Here equilibrium means pressure volume equilibrium. When heat q is supply to system only change in heat of cylinder A , Not in B and C. This is due to between cylinder A and B have adiabatic piston. So no change in heat in B and also further not change in C, so temperature is not change. Because given gas is ideal gas. Ideal gas temperature change only on amount of heat change,it is based on kinetic theory of gases.

Given that Volume of C = V_o/4

Hence given gases is ideal so according to the boyle's law Pressure of the gas is inversely proportional to the volume, Hence pressure of C cylinder is = 4P_o.

Thus pressure and volume of C is 4P_o and V_o/4 .

Similarly between B and C diathermic wall means B and C have same temperature due to diathermic wall , hence thermal equilibrium.

Thus, B have same temperature as C, So we know that gas is ideal means pressure have same value of C and again using boyle's law and volume is same as C cylinder i.e. Thus pressure and volume of B is 4P_o and V_o/4.

At P-V Equilibrium

P_AV_A = (P_B+P_C)(V_B+V_C)

P_AV_A = (4P_o + 4P_o)(V_o/4+V_o/4)

P_AV_A =8P_o*V_o/2= 4P_oV_o

or

P_oV_{o =} P_AV_A /4 ........................................................................(i)

We know that

q=C^m_pT_o ........................................................................(ii)

and we also know that for ideal gas molar Heat capacities difference is

C^m_p-C^m_v = R

Multiply above by T_o and getting

C^m_p*T_o - C^m_v*T_o = R*T_o

putting given value of C^m_v = 2R in above equation and we get

   C^m_p*T_o -2R*T_o = R*T_o

C^m_p*T_o = 3RT_{o .............................................(iii)}

From equation (ii) q is equal to Cm_pT_o , so putting q in equation (iii)

q = 3RT_o ...............................................................(iv)

So the value of according question  P_oV_o /q is

using equation number (i),(iv) and putting above

P_oV_o /q = P_AV_A / (4* 3RT_o) = P_AV_A/12RT_o