What mass of ice taken at -20 degrees Celsius can be turned into water at 20 degrees Celsius by burning 100 grams of gasoline?

We give all the values ​​from given in the SI system:
t1 = -20 C = 253 K.
mt = 100 g = 0.1 kg.
1. The amount of heat required to heat ice and melt is equal to:
Q = Q1 + Q2, where Q1 is the amount of heat required to heat the ice to the melting temperature, Q2 is the amount of heat required to melt the ice.
2. The amount of heat spent on heating the body is equal to the product of the specific heat capacity of the substance, body weight and the difference between the final and initial temperatures.
Q = c * m * (t2-t1), where c is the specific heat capacity of the substance, m is the mass of the substance, t2 and t1 are the final and initial temperatures, respectively.
The specific heat capacity of ice is c = 2100 J / kg * K, the melting point of ice is 0 C = 273 K.
3. To melt the ice, the required amount of heat:
Q = λ * m, where λ is the specific heat of fusion of the substance, m is the mass of the substance.
Specific heat of melting of ice λ – 3.3 * 10 ^ 5 J / kg
4. When fuel is burned, the amount of heat will be released:
Qg = q * mt, where q is the specific heat of combustion of the fuel, m is the mass of the substance.
Specific heat of combustion of gasoline q – 42 * 10 ^ 6 J / kg
5. Substitute everything into the formula from point 1:
q * mt = c * m * (t2-t1) + λ * m.
m = q * mt / (c * (t2-t1) + λ).
6. Substitute the numbers, we have:
m = q * mt / (c * (t2-t1) + λ) = 42 * 10 ^ 6 * 0.1 / (2100 * (273-253) + 3.3 * 10 ^ 5) = 11.3 kg …
Answer: You can melt 11.3 kg of ice.