- #1
tuki
- 19
- 1
- Homework Statement
- In insulated copper container (mass 0.100 kg) there is water (mass 0.160 kg) and ice (mass 0.018 kg) in thermal balance. Lead is being added into container which is at 255 celcius and mass of 0.750kg. What is temperature when container and it's contents reach thermal balance after adding lead?
Some constants:
Copper thermal capacity: 390 J/kgK
Lead thermal capacity: 130 J/kgK
Water thermal capacity: 4190 J/kgK
Ice thermal capacity: 2100 J/kgK
Ice melting temperature: 334*10^3 J/kg
Lead melting point 327.3 Celicus
- Relevant Equations
- Thermal energy:
$$ Q = cm \Delta T $$
Since ΔT is change in temperature, the container and it's contents and the led most have same temperature difference when the led is added. I tried by assuming that energy released by the led is same as the amount that container and it's contents absorb. Meaning Q1-Q2 = 0 => Q1 = Q2.
$$ \Delta T(c_c m_c + c_w m_w) - m_i L = \Delta T(c_l m_l) $$
where _c = copper, _w = water, _i = ice, _l = led, L = Ice melting temperature.
By solving $\Delta T$ from this equation we should be able to figure how much temperature changes. However there are some things in this that don't add up. Now the temperature change should be equal for both except it doesn't? It cannot be equal since wouldn't make sense that both led and container would have same change in temperature.
Getting a little confused with this so maybe someone could help?
Correct answer should be approx 21 celicus
Also could someone tell me how to use latex / mathjax inside text. In mathexchange you can use two dollar signs $$ for math inside text and double for centered equation. However here the only two dollar signs won't work?
$$ \Delta T(c_c m_c + c_w m_w) - m_i L = \Delta T(c_l m_l) $$
where _c = copper, _w = water, _i = ice, _l = led, L = Ice melting temperature.
By solving $\Delta T$ from this equation we should be able to figure how much temperature changes. However there are some things in this that don't add up. Now the temperature change should be equal for both except it doesn't? It cannot be equal since wouldn't make sense that both led and container would have same change in temperature.
Getting a little confused with this so maybe someone could help?
Correct answer should be approx 21 celicus
Also could someone tell me how to use latex / mathjax inside text. In mathexchange you can use two dollar signs $$ for math inside text and double for centered equation. However here the only two dollar signs won't work?