Ice at -10degrees celcius and steam at 130 degrees celcius are brought together at atmospheric pressure in a perfectly insulated container. After thermal equilibrium is reached,the liquid phase at 50 degrees celcius is present. Ignoring the container and the equilibrium vapor pressure of the liquid at 50 degrees celcius, find the ratio of the mass of steam to the mass of ice. The specific heat capacity of steam is 2020 joules per kilogram.degrees celcius

To find the ratio of the mass of steam to the mass of ice, we need to use the principle of energy conservation.

First, let's calculate the heat gained or lost by each substance during the process of reaching thermal equilibrium:

1. Heat gained or lost by ice: To reach thermal equilibrium, the ice needs to be heated from -10°C to 0°C (its melting point) and then undergo a phase change from solid to liquid at 0°C. The specific heat capacity of ice is 2100 J/kg·°C, and the heat of fusion (latent heat) of ice is 333 kJ/kg.

- Heat gained to warm ice from -10°C to 0°C: Q1 = mass of ice × specific heat capacity of ice × change in temperature
Q1 = mass of ice × 2100 J/kg·°C × (0 - (-10))°C
Q1 = mass of ice × 21000 J/kg

- Heat gained during phase change from solid to liquid at 0°C: Q2 = mass of ice × latent heat of fusion
Q2 = mass of ice × 333000 J/kg

The total heat gained by the ice is the sum of Q1 and Q2: Q_ice = Q1 + Q2.

2. Heat gained or lost by steam: To reach thermal equilibrium, the steam needs to be cooled from 130°C to 100°C (its boiling point) and then undergo a phase change from gas to liquid at 100°C.

- Heat lost while cooling steam from 130°C to 100°C: Q3 = mass of steam × specific heat capacity of steam × change in temperature
Q3 = mass of steam × 2020 J/kg·°C × (100 - 130)°C
Q3 = mass of steam × (-60600 J/kg)

- Heat lost during phase change from gas to liquid at 100°C: Q4 = mass of steam × latent heat of vaporization
Q4 = mass of steam × (2.256 × 10^6) J/kg

The total heat lost by the steam is the sum of Q3 and Q4: Q_steam = Q3 + Q4.

Since the container is well-insulated, we know that the heat gained by the ice is equal to the heat lost by the steam:

Q_ice = Q_steam.

Now we can set up the equation and solve for the ratio of the mass of steam to the mass of ice:

mass of ice × 21000 J/kg + mass of ice × 333000 J/kg = mass of steam × (-60600 J/kg) + mass of steam × (2.256 × 10^6) J/kg.

To simplify:

mass of ice × (21000 J/kg + 333000 J/kg) = mass of steam × (-60600 J/kg + 2.256 × 10^6 J/kg).

mass of ice × 354000 J/kg = mass of steam × (2.1954 × 10^6 J/kg).

Dividing both sides by 354000 J/kg:

mass of ice / mass of steam = (2.1954 × 10^6 J/kg) / (354000 J/kg).

mass of ice / mass of steam = 6.204.

Therefore, the ratio of the mass of steam to the mass of ice is approximately 6.204.