What is the minimum power required to operate the heat pump?

AI Thread Summary
To determine the minimum power required to operate a heat pump heating a house at 27 degrees Celsius with an outside temperature of -13 degrees Celsius and a heat loss of 7 kW, the efficiency equation e=Th/(Th-Tc) was applied, yielding an efficiency of 7.5. The calculated power requirement was 933 W, derived from dividing the heat loss by the efficiency. However, there was confusion regarding the units, as the heat loss of 7000 W should have been clearly indicated with units. Clarification on the equation's presentation and unit consistency was suggested to avoid misunderstandings. Accurate unit representation is crucial for validating calculations in thermodynamic applications.
swain1
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Homework Statement


It is proposed to heat a house using a heat pump operating between the house (27 degees) and the outside (-13 degrees). The heat loss from the house is 7kW. What is the minimum power required to operate the heat pump?

Homework Equations


The Attempt at a Solution


e=Th/(Th-Tc) =7.5
W=7000/7.5 =933 W

Just checking if this is correct or have I made a mistake. Thanks
 
Last edited:
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Since you start out with a dimensionless number, a ratio of temperatures, and equate that to some number of Watts, something is surely wrong. Maybe you just need to rewrite things to make it clear
 
I have moved the equation now. If you look at the question you will see that 7000 has units of watts. Is it wrong anyway?
 
swain1 said:
I have moved the equation now. If you look at the question you will see that 7000 has units of watts. Is it wrong anyway?

That looks better. It woudl be better still if you had units of W on the 7000.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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