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# A “clever” technician decides to heat some water for his coffee with an x - ray machine. If the machine produces 10. rad/s, how long will it take to raise the temperature of a cup of water by 50.8 C? Ignore heat losses during this time.

## 2.1 \times 10^{4} s

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##### Andy C.

University of Michigan - Ann Arbor

LB
##### Jared E.

University of Winnipeg

### Video Transcript

for number 47 An X ray machine is gonna be used to heat up a cup of coffee. And the X ray has a read of 10 reds per second. Well, how long would take one over time? Thio to change the temperature of the coffee. 50.8 degrees Celsius. Remember, What I read is a red. By definition, you get 10 to the negative too, Jules per Kilogram. And now this is saying you get that much per second. So if I would take this if I don't know, actually, how much energy I get, I would need to take this 10 and I would need to multiply it by the mass, and I would also need to multiply it by the time. And then that would give me the amount of energy I would end up with from this. And now, if I want to heat up coffee, that's just gonna be a phase change. So I'm gonna use the heat. Would be the mass 10th of specific heat drives a change in temperature. Um, the remember the energy I get is gonna be this 10 times the 10 of the native to so 10 reds attending *** two times 10 gives me 100.1. So 0.1 times the mass, the coffee that I don't know. So I'm just gonna call that mass coffee sometimes the time, which is what I'm trying to find. So this tea is what I'm trying to find over here. This is none of the mass of the coffee specific heat of the coffee, which I can assume is just water. So 41 86. That's the one that's in jewels. And I know my change in temperature has to be 50.8. Um, somebody mask coffee. Doesn't matter. It cancels out of this problem, and I divide, multiply and divide. And so, for this tea and then get T is 2.13 times 10 to the sixth, and that would turn out to be in seconds.

University of Virginia
##### Andy C.

University of Michigan - Ann Arbor

LB
##### Jared E.

University of Winnipeg