To find the mass of steam needed to warm a cup of water, we use the heat equation to calculate the heat needed to raise the temperature of the water and the glass, and then apply the latent heat of vaporization and the specific heat capacity of steam to find the required mass.
To determine the mass of steam that must condense to warm a glass cup and water from 20.0°C to 50.0°C, we need to apply the principles of thermodynamics and heat transfer. First, we calculate the amount of heat required to warm the water and the glass cup. Then, we use the latent heat of vaporization and the specific heat capacity of steam to find the mass of steam.
The heat required to warm the water (Qwater) is given by:
Qwater = mw × cw × ΔT
Where:
- mw = 0.200 kg (mass of the water)
- cw = 4.19 x 10³ J/kg·K (specific heat capacity of water)
- ΔT = 30.0°C (temperature change)
The heat required to warm the glass cup (Qcup) is:
Qcup = mg × cg × ΔT
Where:
- mg = 0.100 kg (mass of the glass cup)
- cg = 837 J/kg·K (specific heat capacity of glass)
The total heat required (Qtotal) is the sum of Qwater and Qcup. The mass of steam (ms) that needs to be condensed can be calculated using:
ms = Qtotal / (cs × (ΔTs) + L)
Where:
- cs = 2.01 x 10³ J/kg·K (specific heat capacity of steam)
- ΔTs = 130°C - 100°C (temperature change from 130°C to 100°C)
- L = 2.26 x 10¶ J/kg (latent heat of vaporisation)