Physics, 02.08.2019 12:30 ANCHUXIA

Determine the final state and temperature of 100 g of water originally at 25.0°c after 50.0 kj of heat have been added to it.

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The quantity of heat needed to increase the temperature of a substance by $\Delta T$ is given by
$Q=m C_p \Delta T$
where m is the mass of the substance and C_p

is the specific heat of the substance. In our problem, we have m=100~g=0.1~Kg

and

, which is the speficic heat of the water.
Therefore, we can find the increase in temperature $\Delta T$ :
$\Delta T = \frac{Q}{m C_p}= \frac{50~KJ}{0.1~Kg cdot 4.19~KJ/(Kg K)}=119~K =119^{\circ}C$
The initial temperature of the water was $25^{\circ}C$ , so the final temperature should be
$T_f = 25^{\circ}C+119^{\circ}C=144^{\circ}C$
So the water should be now vapor.

To be more precise, however, in the transition liquid-vapor part of the heat added to the system is used to break the bonds between molecules, and it does not increase the temperature of the system. The amount of heat needed for the transition between liquid and vapor is given by
$Q=m C_L=0.1~Kg \cdot 2265~KJ/Kg=226.5~KJ$
where C_L

is the latent heat of vaporization of the water.
However, the initial amount of heat added to the water (50 KJ) is smaller than this number, therefore there isn't enough heat to complete the transition liquid-vapor. Therefore, the water will still be in the liquid-vapor change phase at a temperature of $100^{\circ}C$ (which is the temperature at which the phase change starts)

Answer from: hermine40

The final state of the water is vapor (gas) and the final temperature is 144.1 ⁰C.

The given parameters;

Mass of the water, m = 100 gInitial temperature of the water, t₁ = 25 °CHeat added to the water, Q = 50 kJ = 50,000 J

The quantity of the heat added to water to cause a change in the state of the water is given as;

Q = mcΔt

where;

c is the specific heat capacity of water = 4,200 J/kg°CΔt is the change in temperature of the water

The change in temperature of the water is calculated as;

$\Delta t = \frac{Q}{mc} \\\\\Delta t = \frac{50,000}{0.1 \times 4,200} \\\\\Delta t =119.1 \ ^0C$

The final temperature of the water is calculated as;

Δt = t₂ - t₁

t₂ = Δt + t₁

t₂ = 119.1 + 25

t₂ = 144.1 ⁰C.

Thus, the final state of the water is vapor (gas) and the final temperature is 144.1 ⁰C.

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Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

Answer from: Quest

This did i unseated, sorry

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