- #1
Pouyan
- 103
- 8
- Homework Statement
- 1 kg of liquid water with a temperature of 373 K is cooled in a reversible heat engine by a very large block of ice with a temperature of 273 K until the water (still liquid) adopts the temperature of 273 K. Determine how much ice is melted in the process.
- Relevant Equations
- C_w = C_water= 4200 (J/KgK)
dQ_water= 1kg*C_w*dT
C_ice=334000 J/kg
Q_ice= m_ice * C_ice
My attempt:
I though :
ΔQ_w= 1*4200 * (-100) J=-420000J
Q_ice=334000*m_ice = ΔQ_w
But it was totaly wrong!
The solution showed :
Because the heat engine is reversible the efficiency η = 1- (T_cold / T)
T_cold is always 273 K while the hot temperature changes from 373 K to 273 K during this loop.
The amount of heat taken from the ice :
Q = -C ∫(1-(1-(T_cold/T)))*dT [from 373 to 273]
Q=358 kJ
Q_ice=334000*mm=Q/Q_ice = 1.07 kg
My question is this part:
Q = -C ∫(1-(1-(T_cold/T)))*dT
What do I see it is Q=-C*∫(1-η)dT
1-But what does 1-η mean?
2-Where does the negative sign come from? (I mean why do we write -C?)
I though :
ΔQ_w= 1*4200 * (-100) J=-420000J
Q_ice=334000*m_ice = ΔQ_w
But it was totaly wrong!
The solution showed :
Because the heat engine is reversible the efficiency η = 1- (T_cold / T)
T_cold is always 273 K while the hot temperature changes from 373 K to 273 K during this loop.
The amount of heat taken from the ice :
Q = -C ∫(1-(1-(T_cold/T)))*dT [from 373 to 273]
Q=358 kJ
Q_ice=334000*mm=Q/Q_ice = 1.07 kg
My question is this part:
Q = -C ∫(1-(1-(T_cold/T)))*dT
What do I see it is Q=-C*∫(1-η)dT
1-But what does 1-η mean?
2-Where does the negative sign come from? (I mean why do we write -C?)