Question

Two bodies have thermal capacities in the ratio 3 : 4 and the rates of loss of heat in the ratio 3 : 5. Their rates of cooling will be in the ratio of :

• A. 9 : 20
• B. 4 : 5
• C. 5 : 4
• D. 1 : 1

Answer 1

The correct option is B 4 : 5

$\frac{K_1}{K_2}=\frac{3}{4}\frac{{\left(△Q/△T\right)}_1}{{\left(△Q/△T\right)}_2}=\frac{3}{5}$

We know $\frac{△Q}{△t}=\frac{△\theta }{\frac{l}{KA}}$

$\frac{{\left(△Q/△T\right)}_1}{{\left(△Q/△T\right)}_2}=\frac{△{\theta }_1}{\frac{l}{K_{1}A}}\times \frac{\frac{l}{K_{2}A}}{△{\theta }_2}=\frac{3}{5}\Rightarrow \frac{△{\theta }_1}{△{\theta }_2}=\frac{3}{5}\times \frac{K_2}{K_1}\Rightarrow \frac{{\left(△Q/△T\right)}_1}{{\left(△Q/△T\right)}_2}=\frac{3}{5}\times \frac{4}{3}=\frac{4}{5}$