A) 1 cal
B) 80 cal
C) 540 cal
Explanation:
A)
The amount of heat energy needed to raise the temperature of a certain mass of a substance is given by
![Q=mC\Delta T](https://tex.z-dn.net/?f=Q%3DmC%5CDelta%20T)
where
m is the mass of the substance
C is the specific heat capacity
is the change in temperature
In this problem:
m = 1 g is the mass of water
is the specific heat capacity of water
is the change in temperature
So, the heat needed is
![Q=(1)(1)(1)=1 cal](https://tex.z-dn.net/?f=Q%3D%281%29%281%29%281%29%3D1%20cal)
B)
For a solid substance at its melting point, the amount of heat needed to melt completely the substance is given by
![Q=m\lambda_f](https://tex.z-dn.net/?f=Q%3Dm%5Clambda_f)
where
m is the mass of the substance
is the specific latent heat of fusion of the substance
In this problem:
- The ice is already at melting point, 0 °C
- Mass of the ice: ![m=1g](https://tex.z-dn.net/?f=m%3D1g)
- Specific latent heat of fusion of ice: ![\lambda_f=80 cal/g](https://tex.z-dn.net/?f=%5Clambda_f%3D80%20cal%2Fg)
So, the heat needed is
![Q=(1)(80)=80 cal](https://tex.z-dn.net/?f=Q%3D%281%29%2880%29%3D80%20cal)
C)
For a liquid substance at its boiling point, the amount of heat needed to boil completely the substance is given by
![Q=m\lambda_v](https://tex.z-dn.net/?f=Q%3Dm%5Clambda_v)
where
m is the mass of the substance
is the specific latent heat of vaporization of the substance
In this problem:
- The water is already at boiling point, 100 °C
- Mass of the water: ![m=1g](https://tex.z-dn.net/?f=m%3D1g)
- Specific latent heat of vaporization of water: ![\lambda_v=540 cal/g](https://tex.z-dn.net/?f=%5Clambda_v%3D540%20cal%2Fg)
So, the heat needed is
![Q=(1)(540)=540 cal](https://tex.z-dn.net/?f=Q%3D%281%29%28540%29%3D540%20cal)