Question 1

A solid metallic cube having total surface area 24 ~m ^2 is uniformly heated. If its temperature is increased by 10^ C , calculate the increase in volume of the cube. ( . Given : . =5.0 10^ -4 ^ C ^ -

Accepted Answer

We have V=V_0 T V=a^3,(3 ) T Now, 6 a^2=24 [ Total surface area of cube .=6 a^2 ] a^2=4 a=2 So, V=2^3 (3 5 10^ -4 ) 10=1200 10^ -4 ~m ^3 =1200 10^2 ~cm ^3=1.2 10^5 ~cm ^3

Question 2

A bowl filled with very hot soup cools from 98^ C to 86^ C in 2 minutes when the room temperature is 22^ C . How long it will take to cool from 75^ C to 69^ C ?

Accepted Answer

The rate of heat flow is given by aligned & Q t =-K (T-T_0 ) Q t =-K (T_ a v g -T_0 ) \ & Initially T_ a v g = T_1+T_2 2 \ & Here, T_1=98^ C \ & T_2=86^ C aligned aligned & (i) ms 12 2 =- K ( 98+86 2 -22 ) \ & 6=- K ms [ 98+86 2 -22 ] ( Q = ms T ) aligned Now, cool from T _1^ =75^ C aligned & T _2=69^ C \ & T _ avg = T _1^ + T _2^ 2 = 75+69 2 aligned (ii) ms 6 t =- K ( 75+69 2 -22 ) Divide equation (ii) by (i), we have aligned & 6 t(6) = 50 70 \ & t= 7 5 =1.4 ~min aligned

Question 3

The two ends of a rod of length L and a uniform crosssectional area A are kept at two temperatures T_ 1 and T _ 2 ( ~T _ 1 > T _ 2 ). The rate of heat transfer, dQ dt through the rod in a steady state

Accepted Answer

dQ dt = kA ( T _ 1 - T _ 2 ) L [ ( T _ 1 - T _ 2 ) . is the temperature difference ]

Thermal Properties of Matter — Previous Year Questions & Solutions