Question

Heat transfer

1 Normal 1 No Spac.. Heading 1 Heading2 Title Subt Paragraph Styles Heat Transfer - Assignment 1 An ideal gas is heated from 50 C to 80 C, (a) at constant volume and (b) at constant pressure. For which case do you think the energy required will be greater? Why? 1. 2. Consider a house with a floor space of 200 m2 and an average height of 3 m at sea level essure is 101.3 kPa. Initially the house is at a uniform where the standard atmospheric pr temperature of 10°C. Now the electric heater is turned on, and the heater runs until the air temperature in the house rises to an average value of 22°C. Determine how much heat is bsorbed by the air assuming some air escapes through the cracks as the heated air in the house expand at constant pressure. Also, deternine the cost of this heat if the unit cost of electricity in area is $0.075/kWh. 3. Water is heated in an insulated, constant diameter tube by a S kW electrie resistance heater. If the water enters the heater steadily at 150C and leaves at 60 C, determine the mass flow rat of water. WATER 15℃ → 60℃ 5 kW Air enters the duct of an air conditioning system at 100 kPa and 10°C at a volume flow rate of 15 m/min. The diameter of the duct is 24 em and heat is transferred to the air in the duct from the surroundings at a rate of 2 kW. Determine (a) the velocity of the air at the duct inlet and (b) the temperature of the air at the exit. 4. 5. What is the physical mechanism of heat conduction in a solid? a liquid? a gas?

Answer 1

1.

Given : T₁ = 50°c , T₂ = 80°c

Solution:

(a) constant volume

$\delta$ Q = dU + $\delta$ W

$\delta$ Q = dU + pdV

$\delta$ Q = dU + 0 [ volume is constant, so dV=0]

i.e. $\delta$ Q_v = Mc_vdT

Where c_v is the specific heat due at constant volume

(b) Constant pressure

$\delta$ Q = dU+ W

= dU + dPv

= d(U+Pv)

$\delta$ Q = dH

= Mc_pdT

Where c_p is the specific heat at constant pressure.

i.e. $\delta$ Q_P = Mc_pdT

Conclusion:

Since work done is zero in case of constant volume process , all heat supplied is used in increasing the internal energy of the system and temperature rises. But in case of constant pressure process, a part of heat supplied is used in the work done ( or increasing the volume of system). So more amount of energy is required in constant pressure process to increase the temperature of the gas.

Also we know that , c_p > c_v , so more amount of energy is required for constant pressure process.