Question

One end of metal bar of area of cross section 5cm${}^2$ and 25 cm in length is in steam other in contact with ice, the amount of ice melts in one minute is ( L $=$ 80 cal /gm; K=30W/m K)

• A. 1.6 gm
• B. 1.07 gm
• C. 2.4 gm
• D. 36 gm

Answer 1

The correct option is B 1.07 gm

Given

Area of cross-section of rod=$5{cm}^2=5\times {10}^{-4}{m}^2$

Length of rod=$25cm=25\times {10}^{-2}m$

Thermal conductivity, K=$30W/mK$

$L=80cal/gm$

$\frac{△Q}{△t}=\frac{△\theta }{\frac{l}{KA}}\to 100$

$=\frac{100}{\frac{25\times {10}^{-2}}{30\times 5\times {10}^{-4}}}$

$=6J/s$

For 1 min

$△Q=360J$

$m\times 80\times 4.2=360m=1.07g$