When you mix two substances, the heat gained by one substance is equalto the heat lost by the other substance. Suppose you place 125 g of aluminum ina calorimeter with 1,000 g of water. The water changes temperature by 2 °C andthe aluminum changes temperature by â74.95 °C. Required:
a. Water has a known specific heat capacity of 4.184 J/g °C. Usethe specific heat equation to find out how much heat energy the watergained (q).
b. Assume that the heat energy gained by the water is equal to the heat energy lost by the aluminum. Use the specific heat equation to solve for the specific heat of aluminum. (Hint: Because heat energy is lost, the value of q is negative.)

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue

Explain why electric current cannot exist if a current doesn't have a voltage source.

Hydrogen atoms are excited by a laser to the =4n=4 state and then allowed to emit. what is the maximum number of distinct emission spectral lines (lines of different wavelengths) that can be observed from this system? 8 6 2 7 4 5 1 3 calculate the wavelength of the 4⟶14⟶1 transition. =λ=