An insulated rod (length = 60 cm, area = 1.25 cm^2 has one end maintained at 100

Question

An insulated rod (length = 60 cm, area = 1.25 cm^2 has one end maintained at 100 degree C while the other end is maintained at 0 degree C by inserting in an ice-water mixture. If 8.5 g ice (L_f = 3.34x10^5 J/kg) melts in 10 min, of what should be the thermal conductivity of metal rod? 50.2 W/m. K. 109 W/m. K 148 W/m. K 187 W/m. K 227 W/m. K A container is filled with a mixture of helium (light molecules) and oxygen (heavy molecules) gases. A thermometer in the reads 22 degree C. Which gas molecules have the greater average speed? It is the same for both of the gases because the temperatures are the same. The oxygen molecules do because they are diatomic. The oxygen molecules do because they are more massive. The helium molecules do because they are less massive. The helium molecules do because they are monatomic.

Explanation / Answer

1) L = 60 cm, A = 1.25 cm^2, T1 = 100 oC , T2 = 0 oC

energy released while ice is melting Q = mL

Q/t = mL/t

Q/t = K*A(T1 -T2)/L

0.0085*3.34*10^5/(10*60) = K*1.25*10^-4*(100-0)/0.6

K = 227 W/m.K

correct option is (E)

2) vrms = (3RT/M)^0.5

Here M is molar mass

M(He) = 4 g/mol

M(O2) = 32 g/mol

M(He) < M(O2)

so (vrms)He > (vrms)O2

(vav)He > (vav)O2

correct otpion is (D)

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