Question

A box with sides of length 40 cm is made up of six pieces of concrete of thickness 5 mm. The inside of the box is filled with 100 moles of a diatomic ideal gas while the temperature outside the box is 30°C. At what rate is the temperature of the gas increasing when the gas is at -40°C? (The thermal conductivity of concrete is 0.33 W/(m×K).)a) 1.22 °C/s b) 1.45 °C/s c) 1.68 °C/s d) 2.13 °C/s e) 2.90 °C/s

Answer 1

d)2.13 C s⁻¹

Step-by-step explanation:

Rate of flow of heat through walls

=
`(KA(T_2-T_1))/(d)`

K = .33

A = 6 X .4 X .4 =0.96

T₂-T₁ = 30+40 = 70

d = 5 x 10⁻³

Put these data in the relation above

Rate of flow of heat

=
`(.33*.96*70)/(5*10^(-3))`

= 4435.2 Js⁻¹

Specific heat of gas = 2.5 R = 20.785 J

Rise in temp =
`(4435.2)/(100*20.785)`

= 2.13 degree celsius.