Find the final temperature of the ball

AI Thread Summary
To find the final temperature of a copper ball with a radius of 1.5 cm that has expanded due to heating, the coefficient of linear expansion for copper is utilized, which is 17 x 10^-6. The coefficient of volume expansion is determined to be three times this value. The volume change is calculated to be approximately 0.54. Initially, there was confusion regarding the application of the equation delta V = BV(delta T), but the correct approach involves adding the room temperature of 22°C to the calculated temperature change. The final temperature of the ball is confirmed to be 410.27°C.
dphoos
Messages
6
Reaction score
0
A copper ball with a radius of 1.5 cm is heated until its diameter has increased by 0.20 mm. Assuming a room temperature of 22°C, find the final temperature of the ball.
 
Physics news on Phys.org
What have you tried?
 
well, I know that the coefficient of linear expansion for copper is 17 x 10^-6, so it's coefficient of volume expansion is 3 times that.. and I know that the volume has changed by about .54. I'm not really sure what to do with this though
 
I assume I'm using the equation delta V = BV(delta T), but when I do this I get a huge number
 
nevermind, I got it. I was subtracting 22 instead of adding it. The answer is 410.27 right?
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top