Question

Water has the following thermodynamic constants: (1) specific heat liquid = 4.18 J/g °C, solid = 2.09 J/g °C, gas = 1.89 J/g °C, (2) heat of fusion = 334 J/g, and (3) heat of vaporization = 2257 J/g. For a sample of water at 1.0 atm of pressure, mass = 230 g at an initial temperature of -47 °C and a final temperature of 350 °C, answer the following questions: (1) how much heat is required to warm the solid sample to its melting point? J (2) how much heat is required to melt the sample? J (3) how much heat is required to warm the liquid sample to its boiling point? J (4) how much heat is required to vaporize the sample? J (5) how much heat is required to warm the gaseous sample to its final temperature? J and finally, (6) how much heat is required for the entire process to occur

Answer 1

823337.9 J

Step-by-step explanation:

At 1atm of pressure, water's melting point is about 0°C and its vaporization point is 100°C.

(1) At -47°C, water will be in solid state. The heat that is required to warm the solid sample to its melting point is given by:

`Q = m*sh*(T_f-T_o)`

Where sh is specific heat at solid, that tells us the heat per unit of mass required to increase the temperature 1°C at solid state:

`Q = 230 g * 2.09 (J)/(g^oC) *(0^oC - -47^oC) = 22592.9 J\\`

(2) The heat is required to melt the sample is given by:

`Q = m*cl`

Where cl is the heat of fusion, that tells us the heat per unit of mass to fuse or freeze water.

`Q = 230g* 334 J/g = 76820 J`

(3) The heat that is required to warm the liquid sample to its boiling point is given by:

`Q = m*sh*(T_f-T_o)`

Where sh is specific heat at liquid. that tells us the heat per unit of mass required to increase the temperature 1°C at liquid state:

`Q = 230 g * 4.18 (J)/(g^oC) *(100^oC - 0^oC) = 96140 J\\`

(4) The heat that is required to vaporize the sample is given by:

`Q = m*cl`

Where cl is the heat of vaporization, that tells us the heat per unit of mass to vaporize or condense water.

`Q = 230g* 2257 J/g = 519110 J`

(5) The heat that is required to warm the gas sample to its final temperatur is given by:

`Q = m*sh*(T_f-T_o)`

Where sh is specific heat at gas. that tells us the heat per unit of mass required to increase the temperature 1°C at gas:

`Q = 230 g * 1.89(J)/(g^oC) *(350^oC - 100^oC) = 108675 J\\`

(6)The heat that is required for the entire process to occur is simply the addition of all the heats calculated:

`Q = Q_1 + Q_2 + Q_3 + Q_4 + Q_5\\Q = 22592.9 J + 76820 J + 96140 J + 519110 J + 108675 J = 823337.9 J`

or 823.34 kJ