A furnace for processing semiconductor materials is formed by a silicon carbide chamber that is zone-heated on the top section and cooled on the lower section. With the elevator in the lowest position, a robot arm inserts the silicon wafer on the mounting pins. In a production operation, the wafer is rapidly moved toward the hot zone to achieve the temperature-time history required for the process recipe. In this position, the top and bottom surfaces of the wafer exchange radiation with the hot and cool zones, respectively, of the chamber. The zone temperatures are Th 1500 K and Tc 330 K, and the emissivity and thickness of the wafer are 0.65 and d 0.78 mm, respectively. With the ambient gas at T 700 K, convection coefficients at the upper and lower surfaces of the wafer are 8 and 4 W/m2 K, respectively. The silicon wafer has a density of 2700 kg/m3 and a specific heat of 875 J/kg K. (a) For an initial condition corresponding to a wafer temperature of Tw,i 300 K and the position of the wafer shown schematically, determine the corresponding time rate of change of the wafer temperature, (dTw/dt)i . (b) Determine the steady-state temperature reached by the wafer if it remains in this position. How significant is convection heat transfer for this situation? Sketch how you would expect the wafer temperature to vary as a function of vertical distance.
Macroeconomics 3/18/2016 GDP= C + I + G + (Xg – M ) - C Consumer Spending - I Investment Spending This is NOT Buying Stocks and Bonds Spending by Businesses (mostly) 1. New tools, equipment, machinery, factories (new capital) 2. Residential Spending – (buying a new home) 3. Changes in Inventory - G Government Spending Spending by all levels of government Excludes transfer payments (purely financial transactions) - Exports (gross Xg) : Our stuff to others - Imports (M) : Their stuff to us Components of GDP - Consumptions - Consumer spending Is the biggest component of total spending 70 – 75% - Spending by households on: 1. Durable goods: 11% - goods that last 1-3 years computers, cars, appliances, cell phones, electronics, instruments, and books 2. Nondurables : 29% - consumables – less than a year : food, alcohol, tobacco, toiletries, medication, fuel products 3. Services : 60% - things you pay to do for you : legal services, personal grooming, home repair services, restaurants, car services Factors that determine consumption 1. Income - Income is the most important determinant of consumer spending remember circular flow of economic activity - Output = income - Producing stuff generates income for people- consumers, businesses, and governments - Disposable income : income after savings - Disposable income: consumption + saving - Saving is not spending Macroeconomics 3/21/2016 Factors that determine consumption … Continued - Consumer spending 1. Income (continued…) Disposable income: income after taxes Disposable income = consumption + saving More income means more consumption and more saving (less income = less of both) 2. Prices (Walmart and gas prices) Higher prices reduce consumption Lower prices increase consumption You feel “richer” with LOWER prices 3. Wealth Effects: amount of accumulated wealth a person has will (may Should) affect a person’s ability and willingness to spend now Changes in wealth can change consumer behavior Wealth: value of financial assets such as stock portfolios and retirement accounts and value of real assets - - your home, car VERY IMPORTANT: The best measure of wealth is net-worth- value of assets (home, bank, accounts, portfolio, etc.) MINUS liabilities (claims) {mortgages credit card, debt, loans – school Car} Important accounting tool: balancing sheet Assets Liability (bank claim) and Owners equity 1) $200,000 $200,000 - “0” 2) $300,000 $200,000 3) $200,000 $200,000 - OWE $100,000 Asset example: VALUE OF HOME = $200,000 Liability: VALUE OF MORTGACE LOAN = $200,000 Assume you buy a home for $200,000 and borrow $200,000 Wealth effects using balance sheet 1. Home purchased using mortgage loan - Owner equity = 0 2. Assume home prices rise - Home equity loan or Second Mortgage ($100,000) 3. Home Prices Fall - You owe more than value of home {upside down or under water} 4. Credit Conditions - Availability of credit and interest rates, impact how much households spend- - Easy credit and low rates encourage consumption - Tight credit and high rates discourage consumption 5. Taxes- change disposable income - Increase taxes decrease consumption - Decrease taxes increase consumption 6. Expectations
