Specific Heat Capacity Question

[Timiop2008]

A bath contains 110 litres of water where 1 litre has a mass of 1kg.

a) Given that the specific heat capacity of water is 4200JKg^-1K^-1, calculate the energy required to raise the temperature of the water from 10'C to 40'C.

b) As the water flows through the copper pipes, it is heated from 10'C to 40'C by a gas flame The water flows at 5kg per minute. Calculate the rate of energy transfer to the water.

Attempt:
a) Q=mcT
Q=30 x (110X4200)
Q= 1.38X10⁷J

b) Rate of energy transfer = Power
Power = W/t ?

 

[anathema]

Power = 110 x 5/60
Power = 9.17 W/min

Hello!

Thank you for sharing your calculations. I would like to confirm that your calculations are correct. In part a), you correctly used the formula Q=mcT to calculate the energy required to raise the temperature of the water. In part b), you correctly used the formula Power = W/t to calculate the rate of energy transfer to the water. I would also like to add that the specific heat capacity of water is typically given in units of J/gK, so it is important to convert the mass from kg to g in your calculations. Keep up the great work!

 

[kerimek]

Power = (5kg/min)(4200J/kg)(40-10)/60 = 7000J/s or 7kW

I would like to clarify that the units for specific heat capacity are J/kgK, not JKg-1K-1. This is a common mistake and it is important to use the correct units in order to obtain accurate calculations.

Also, it is important to note that for part a), the mass of the water should be 110kg, not 30kg. The correct calculation would be:

Q = mcΔT
Q = (110kg)(4200J/kgK)(40-10)
Q = 1.38x10^7 J

For part b), the rate of energy transfer is also known as power, which is measured in watts (W) or joules per second (J/s). So the correct calculation would be:

Power = (5kg/min)(4200J/kgK)(40-10)/60s
Power = 7000J/s or 7kW

It is important to pay attention to units and use the correct equations in order to obtain accurate results in scientific calculations.