Hot gas enters a heat exchanger at 200°C and leaves at 150°C. The cold air enters at 40°C and leaves at 140°C. The capacity ratio of the heat exchanger will be:

Concept: 

The heat capacity of the fluid is the product of mass flow rate and the specific heat of the fluid. 

The capacity ratio in the heat exchanger is the ratio of minimum heat capacity to the maximum heat capacity

Capacity Ratio \(R = \frac{{{C_{min}}}}{{{C_{max}}}}\)

In a heat exchanger  

Heat released by hot gas = Heat gained by cold gas

ṁ_h C_ph (T_hi - T_he) = ṁ_c C_pc (T_ce - T_ci)

Calculation:

Given, T_hi = 200°C, T_he = 150°C, T_ce = 140°C, T_ci = 40°C

Now,

ṁ_h C_ph (200 - 150) = ṁ_c C_pc (140 - 40)

ṁ_h C_ph × 50 = ṁ_c C_pc × 100

clearly cold fluid capacity is less compared to hot fluid

\(R = \frac{{50}}{{100}}= 0.5\)