Question

Heat is extracted from a certain quantity of steam at

100degrees C. As a result, the steam changes into ice at 0.0degrees
C. If this energy were used to accelerate the icefrom rest, what
would be the linear speed of ice? Forcomparison, bullet speeds of
about 700 m/s are common.

Answer 1

Answer:
`v=2452.91 m/s`

Step-by-step explanation:

Given

initially steam is at
`100^(\circ)C` and converted to
`0^(\circ) C` ice

Let m be the mass of steam

latent heat of fusion and vaporization for water is

`L_f=3.33* 10^5 J/kg`

`L_v=2.26* 10^6 J/kg`

Heat required to convert steam in to water at
`100^(\circ)C`

`Q_1=m* L_v=m\cdot 2.26* 10^6 J`

Heat required to lower water temperature to
`0^(\circ)C`

`Q_2=m* c* \Delta T`

`Q_2=m* 4.184* (100)`

`Q_2=4.184m* 10^5 J`

Heat required to convert
`0^(\circ)C` water to ice at
`0^(\circ)C` is

`Q_3=m* L_f`

`Q_3=m* 3.33* 10^5=3.33m* 10^5 J`

`Q=Q_1+Q_2+Q_3`

`Q=(2.26+0.4184+0.33)m* 10^6 J`

`Q=3.0084m* 10^6 J`

So this energy is equal to kinetic energy of bullet of mass m moving with velocity v

`Q=(1)/(2)mv^2`

`3.0084m* 10^6=(1)/(2)mv^2`

`v^2=3.0084* 2* 10^6`

`v=2.452* 10^3 m/s`

`v=2452.91 m/s`